Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the integral-as-accumulation-function. This is based on the notion of accumulation in general and the notion of accumulative distance function in particular. Through a case-study methodology we investigate how this approach elicits 11th grade students’ mathematical thinking and reasoning. The results show that the integral-as-accumulation-function has potential, since the notions of accumulation and accumulative function can provide a strong intuition for mathematical reasoning and engage students in mathematical dialogue. Implications of these results for task design and further research are discussed.
For many years, teachers’ intuitive evaluations of pupils’ competences was considered to be a solid base for decisions; it is only recently that teachers have been expected more and more to use data. We state that insights on intuitive and data-driven approaches need to be integrated to understand and support informed, professional decisions in education. Starting from an integrated framework we studied teachers’ decision process regarding the transition of 30 pupils during their last year of primary education within a case study design. Results describe different approaches to decision-making. Some teachers greatly rely on intuitive processes when they ultimately make the decision, even if data was collected. Other teachers combine and weigh information deriving from deliberate processes of data use and from intuitive recognition before they decide. Implications for theory and practice are explained.
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One might wonder how intuitive art can connect to neuroscience and how this could be accomplished. In this descriptive article, research connecting art therapy and neuroscience has been collected and a workshop on Intuitive Painting has been described in detail. The connection was made by the author based on an article by Barker (2017), ‘4 Rituals to be more Happy,’ who writes a popular science blog. The rituals: gratefulness, expressing negative emotions, decision making and human touch were combined with Dr. Pinkie Feinstein’s method of Intuitive Painting in a small group setting. Although subjective, it would seem that at least for that moment in time, a small amount of happiness was achieved through combining art and science.
On a societal scale, the ‘problem with work’ is that everyone is exhausted, job security has been replaced by ‘flex work’ and much important work had been invisibilised. While billions of people are displaced and illegalized from work, others have physical/ mental conditions caused by work. The problem with work merits scrutiny not only from medical, corporate or legal perspectives. It needs tackling without an agenda of productivity, with an open regard and embodied, intuitive research. Artistic research has this scope. It taps into knowledges that are underused/repressed, by involving the body, harnessing intuition, experience and situatedness, and activating a plurality of voices. The aim of this research is to gain a deeper understanding of what is (not) work, who we are when we perform work, and when we don’t or are not able to work. Why are certain activities or roles called work and what happens when the term is applied to activities that are not normally deemed work, but which include comparable elements? Three research questions are addressed: 1. What can be learned about work by regarding every job, or all the work, as a performance? 2. What can be learned about performance (art) by looking at it through the lens of work? 3. What are ethical practices in collaborative and participative work processes? The research is carried out through an artistic approach that contains a particular way of making, teaching and researching which is collaborative, performative and transdisciplinary. It proposes the body as a thinking apparatus, experience as a way of gathering information and doing, writing, exchanging and performing as both method and dissemination. This research aims to contribute to a better understanding of what work is in our lives. The research has social, artistic and educational targets and target groups, which are also intertwined.
